Louise Larking has a faraway look in her eyes. “I’d love to do some yarnbombing,” she says. “That’d be fun, wouldn’t it? Yarnbomb a groyne.” Moments ago, I had no idea what yarnbombing – also known as guerrilla knitting – was, still less that you might bombard Kentish coastal defences with it. But in a small terraced house in Whitstable, some unlikely ideas are brewing. Joanne Bartley, whose house this is, has called a meeting to finalise a big event this weekend. Larking is hosting a craft workshop; friend Amy Turner is holding a poetry session; and Bartley plans to build a scale model of Whitstable out of cardboard boxes. The lounge is already crowded with Lilliputian terraced houses and shops. Time is at a premium, not to mention space. Everyone agrees: yarnbombing must wait.

The project, called Fun Palaces, has been brought to life by the writer and theatre-maker Stella Duffy. Today, Duffy is on a last-minute tour of select participants to check how they’re shaping up. I’ve been invited along. “It’s nearly 130 events now, but it’s growing all the time,” she says, giving a cheerful shrug as we head back to the car. “I’ll be honest: no one entirely knows.”

Littlewood and Price’s “laboratory of fun” remained on paper; after years scouring London for a site and the money, they gave up. But the idea persisted. Pondering a way to celebrate Littlewood’s centenary in 2014, Duffy hit upon the Fun Palace idea. She put out a call for other theatre-makers to organise temporary Fun Palaces, expecting she might get a handful; to her astonishment, the movement grew and grew, fed by Twitter and Facebook. Institutions like the Royal Shakespeare Company and Turner Contemporary in Margate volunteered to throw open their doors, as did tiny local volunteer groups.

The fact that Littlewood’s Palace was never actually completed has liberated them to experiment, says Duffy: “We had the freedom to adulterate it. We’re not trying to raise a vast building – we have plenty of cultural buildings already. We just don’t always use them very well.”

In Folkestone, on the other side of Kent, a Fun Palace will occupy the purposefully unpalatial structure of two shipping containers and a salvaged truck trailer, installed in what used to be a carpark on the harbourfront. When Duffy and I arrive, one container is being reconfigured as a fort, complete with crenellations and foghorn. It’s a work in progress – I haven’t seen this much high-speed carpentry since Challenge Anneka – but currently on the schedule are a campfire, Japanese storytelling and giant origami, organised by the town’s Quarterhouse arts centre, Folkestone Fringe and a slightly wild-eyed team of recruits.

“It’s much more than an open day,” explains Quarterhouse director Allegra Galvin. “It alters your relationship with people who visit. Instead of being an audience, they become makers.” What would she like the weekend to be? “A Burning Man for Folkestone. But maybe a bit smaller-scale.”

A favourite Littlewood mantra was her belief “in the genius in every person”; she devised plays for and about working-class audiences, based in the unglamorous surroundings of the Theatre Royal, Stratford East. Despite her commercial successes (most famously Oh What a Lovely War! and her 1958 production of Shelagh Delaney’s A Taste of Honey), she remained convinced that too many galleries and theatres were essentially stately homes run by unrepentant snobs. The Fun Palace was her attempt at an October Revolution.

Duffy emphasises that it’s a group effort (with nine part-time staff based in London), but it’s clear the project would not have got anywhere without her. She has worked as an improviser, director and actor as well as a writer; Fun Palaces has been organised, with Littlewood-ish energy, between completing drafts for her latest novel, a collection of short stories and transferring a show to New York. Life was further complicated earlier this year, when Duffy was diagnosed with a recurrence of breast cancer; her recovery is progressing well, but it has clearly had an effect. “It makes you aware of time,” she says crisply. “There’s a lot I want to get done.”

Our final destination is Deptford, London, where, masterminded by the Albany arts centre, seven organisations are curating activities that will pop up over the borough all weekend, including flashmobs, acrobatics, a story-collecting project and a food fight. In a square in front of the Deptford Lounge library, technicians wearing forensic suits are busy recreating a crime scene – a giant-sized murder mystery, inspired by Deptford’s mythical past. When we finally get there, a crack squad of seven- and eight-year-olds is stress-testing the project, clambering over the scenery and stomping around for clues. Local residents look both absorbed and pleasantly baffled.

“People talk a lot about access,” Duffy says, “but it’s about more than making tickets £10. Culture is about everything: how we talk to each other, who we have a cup of tea with. Fun Palaces is all about openness. There’s so much conversation about that right now.”

And this weekend’s Fun Palaces won’t be the last, she hopes: her dream is that they will become a permanent part of the calendar – an annual opportunity for artists and scientists across the globe to collaborate, for hare-brained schemes to be indulged, and when even the most revered cultural institutions can let their hair down and go a little crazy for the weekend.

She smiles sweetly. “In 10 years’ time, it’d be really cool if it all just happened. Wouldn’t that be great? That’s what Joan would want.”

• This article was amended on 2 October 2014. It originally stated the “giant-sized murder mystery” was happening outside Peckham Library; this has been corrected to Deptford Lounge, which is hosting the event.